The Schmidt rank of a nonzero vector in a tensor product is the number of its nonzero Schmidt coefficients. Equivalently, it is the matrix rank of the coefficient matrix after bases are chosen, and is therefore independent of the choice of bases. A pure bipartite state is unentangled exactly when its Schmidt rank is 1 (Nielsen and Chuang 2000).
Schmidt Rank
See also
Basis, Coefficient Matrix, Matrix Rank, Schmidt Coefficients, Schmidt Decomposition, Tensor Product, VectorExplore with Wolfram|Alpha
References
Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. Cambridge, England: Cambridge University Press, 2000.Cite this as:
Weisstein, Eric W. "Schmidt Rank." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchmidtRank.html